Map Projections

I remember back in middle school my geography teacher taking an intact orange peel (I still wonder how he was able to remove it in nearly one perfect piece) and slamming it up against the chalk board. Flattening the once round peel against the board caused it to tear apart in several places, and even then it wouldn’t lay completely flat against the board.

The teacher’s point, of course, was that a 3-dimensional sphere like the Earth, or an orange, cannot be translated onto a 2-dimensional surface without completely ripping it apart or producing significant distortion. Such has been the dilemma of cartographers for centuries, who have tried in vain to create a 2d map free of distortion or error.

Map projections were developed as a way to represent the 3d earth on a 2d surface while (in most cases) minimizing some type of distortion at the expense of others. Which map projection is used (such as in a GIS) really depends on what the map-maker intends to do with the map. For example, suppose you want to calculate the population density for all the counties in a particular state. Population density is the number of people per area, so it’s critical that the area of the counties are as accurate as possible. In this case you would want to use an equal-area map projection, which maximizes the accuracy of area at the expense of both shape and distance. We’ll start by looking at map projections classified by the type of distortion, either shape, area, distance or direction, they attempt to minimize.

Equal-Area (or equivalent) Projections

Examples: Albers conic, Gall-Peters, Lambert equal-area, Mollweide

Shape distortion is greatest toward the poles.

Equal-area projections, as mentioned above, preserve the accuracy of area at the expense of shape and distance. These types of projections are particularly useful in a variety of spatial analyses where area is an important variable – such as when calculating population density. The Albers projection is one of the most common projections used by cartographers and geoscientists. Although the Albers projection does not preserve shape or distance, the distortion between the maps two standard parallels (lines of latitude) is relatively minor, giving the map a more “realistic” appearance. It is no surprise then that the Albers projection is used often by governments; it is a favorite among the U.S. Census Bureau, the U.S. Geological Survey, and is the standard projection of British Columbia.

Albers equal-area conic projection. Source: USGS.

Conformal (or orthomorphic) Projections

Examples: Mercator, Lambert conformal conic, Peirce quincuncial, Stereographic

Conformal projections, also known as orthomorphic projections, attempt to conserve shape. They are reasonably successful at accomplishing this at relatively small scales (such as an area the size of U.S. state or smaller). At the larger national or continental scale, however, shapes can become significantly distorted even when using a conformal projection.

In the Mercator projection, size is increasingly distorted toward the poles.

One of the best known conformal projections (and one of the best known and most widely used projections, period) is the Mercator projection. Developed by the Flemish cartographer Gerardus Mercator in 1569, the map – like all cylindrical projections – has straight and perpendicular lines of latitude and longitude (parallels and meridians) causing the map to stretch in both the east-west and north-south direction when moving away from the equator. The distortion of size thus becomes greater toward the poles, causing the landmasses nearer the poles to appear much larger than they actually are. Beyond about 70° north or south latitude, the map distortion renders the map unusable.

Some cartographers believe that the Mercator map projection has been far too popularized; with the general public largely unaware of the map’s limitations, people may adopt a highly distorted view of the globe. Greenland, for example,  appears to be roughly the same size as Africa on the Mercator map, but is in reality about only about 1/14th its size.

The classic Mercator projection, with Greenland and Africa roughly the same size.

Equidistant Projections

Examples: Azimuthal equidistant, Equirectangular, Sinusoidal, Werner cordiform

As you can probably guess, equidistant projections preserve distance. Technically, they preserve the distances of great circles, which are formed by passing a plane through the center of the Earth. Unfortunately, like any projection, accuracy is not uniform throughout the entire map. Distances are accurate from any single point to all other points, and fairly accurate from any number of points located close to one another. However, the accuracy of distance falters between a large number of points over a wide area. The conservation of distance, even on an equidistant projection, is not global.

Azimuthal equidistant projection. All points have the correct direction from the center point.

The equirectangular projection is a relatively simple map projection believed to have been developed in 100 AD by Marinus of Tyre. The projection preserves distances along the meridians or lines of longitude. It has become a popular projection used in computer programs because of the relatively simple relationship between locations on the map and locations on the surface of the Earth.

Equirectangular projection.

Azimuthal Projections

Examples: General perspective, Gnomonic, Orthographic, Winkel Tirpel

Azimuthal projections show true directions for a single central point to all other points on the map. The directions, or azimuths, from any other point on the map other than the central point are less accurate and may contain significant error. The accuracy of an azimuth projection does not come at the cost of other accuracies such as shape, distance, or size.

The Winkel Tripel modified azimuthal projection was adopted by the National Geographic Society in 1998.

The Winkel Tripel projection, is a modified azimuthal projection developed by Oswald Winkel in 1921. It has become a favorite among cartographers and geographers as it presents a balance between shape, direction, and size. In 1998, it replaced the Robinson projection as the standard projection of the National Geographic Society. It has since been adopted by many geographic publications and textbooks.

 

The Robinson project doesn’t conserve shape or size perfectly, but does a pretty good job at both.

 

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